A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1 t2 is:

Question

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1 t2 is: (A) R/g (B) R/4g (C) 2R/g (D) R/2g

Tardigrade Admin · Accepted Answer

Range will be same for time t1 t2, so angles of projection will be 'θ' '90° - θ ' t1 = (2u sinθ/g) t2 = (2u sin(90° -θ)/g) and R = (u2 sin 2θ/g) t1t2 = (4u2 sinθ cosθ/g2) = (2/g) [(2u2 sinθ cosθ/g)] a= (2R/g)

Q. A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1​ and t2​ are the values of the time taken by it to hit the target in two possible ways, the product t1​t2​ is:

R/g

R/4g

2R/g

R/2g

Range will be same for time t1​ & t2​, so angles of projection will be ′θ′ & ′90∘−θ' t1​=g2usinθ​t2​=g2usin(90∘−θ)​ and R=gu2sin2θ​ t1​t2​=g24u2sinθcosθ​=g2​[g2u2sinθcosθ​] a=g2R​

Q. A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_{1}$ and $t_{2}$ are the values of the time taken by it to hit the target in two possible ways, the product $t_{1} t_{2}$ is: